Curve Tracing and Rectification of Curves
December 8, 2016Rectification of plane curve when its equation is in polar form r=f(θ) 1. r = f(θ) $s = ∫↙{θ_1}↖{θ_2} √{r^2... View Article
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Differentiation Under the Integral Sign and Error Functions
December 8, 2016Rule I: Integral with limits (a, b) as constants If I(α) = $∫↙{a}↖b f(x, α) dx, then {dI}/{dα} = ∫↙{a}↖b... View Article
Reduction Formulae, Beta and Gamma Functions
December 8, 2016Reduction formulae for sinusoidal functions 1. To find reduction formula for $∫ sin^n x dx$, n is positive integer ≥... View Article
Fourier Series
December 8, 2016Fourier Series f(x) = $a_o/2 + ∑↙{n =1 }↖∞ (a_n cos nx + b_n sin nx)$ $a_o, a_n, b_n$ are... View Article
Applications of Differential Equations
December 8, 2016Rule to find the equation of orthogonal trajectories Note: Differentiate as many times as there are constants. For rectangular cartesian... View Article
Differential Equations
December 8, 2016Order of differential equation Definition: The order of differential equation is the order of highest derivation that appears in the... View Article
List of Formulas
December 8, 2016List of Formulas (1) $∫ x^n dx = {x^{n+1}}/{n + 1} + c$ (2) $∫ 1/x dx = log|x| +... View Article
Friction
December 8, 2016Coefficient of Static Friction $μ_s = {F_s}/{R}$ …For impending motion Coefficient of Kinetic Friction $μ_k = {F_k}/{R}$ For actual motion... View Article
Analysis of Frames
December 8, 2016There are as such no formulas in this chapter. Pratik KatariaPratik Kataria is currently learning Springboot and Hibernate. Technologies known... View Article
Analysis of Cables
December 8, 2016To find tension at extreme points of cable/at support: T = $R_A$ = $√{{A_x^2}+{A_y^2}}$ tan θ = ${A_y}/{A_x}$ For finding... View Article